Concrete admixture compositions are used for the preparation of concrete having anti-washout properties under water, for which self-levelling property is important, for example, used for underwater concrete or for tunnel construction. In order to maintain the properties of a fresh concrete or fresh mortar in good condition, it is necessary to concurrently use a thickening agent. Where conventional thickening agents, for example, methyl cellulose type thickening agent is used, sufficient early strength of the concrete cannot be obtained due to the heavy setting retardation. Also when a pseudo-polymer type thickening agent formed by electrostatic association of two kinds of surfactants is used (e.g., Patent Document 1, Patent Document 2), the resulting concrete has high viscosity and shows poor pumpability. On the other hand, polysaccharide type thickening agents generally are in powdered form and manually added into the mixers, which renders precise control of addition of their minor amount difficult. Moreover, when the thickening agent is used without complete dissolution of the polysaccharide particles, dissolution of the powder particles in the concrete takes time, and relatively longer mixing time is required for attaining the desired segregation-decreasing effect or thickening effect, calling for addition of an increased amount of the thickening agent, which is uneconomical.